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(* Title: Provers/clasimp.ML
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ID: $Id$
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Author: David von Oheimb, TU Muenchen
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Combination of classical reasoner and simplifier (depends on
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simplifier.ML, splitter.ML classical.ML, blast.ML).
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*)
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infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2 addsimps2 delsimps2;
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infix 4 addSss addss;
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signature CLASIMP_DATA =
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sig
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structure Simplifier: SIMPLIFIER
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structure Splitter: SPLITTER
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structure Classical: CLASSICAL
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structure Blast: BLAST
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sharing type Classical.claset = Blast.claset
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end
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signature CLASIMP =
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sig
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include CLASIMP_DATA
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type claset
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type simpset
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type clasimpset
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val addSIs2 : clasimpset * thm list -> clasimpset
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val addSEs2 : clasimpset * thm list -> clasimpset
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val addSDs2 : clasimpset * thm list -> clasimpset
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val addIs2 : clasimpset * thm list -> clasimpset
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val addEs2 : clasimpset * thm list -> clasimpset
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val addDs2 : clasimpset * thm list -> clasimpset
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val addsimps2 : clasimpset * thm list -> clasimpset
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val delsimps2 : clasimpset * thm list -> clasimpset
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val addSss : claset * simpset -> claset
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val addss : claset * simpset -> claset
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val CLASIMPSET :(clasimpset -> tactic) -> tactic
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val CLASIMPSET' :(clasimpset -> 'a -> tactic) -> 'a -> tactic
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val clarsimp_tac: clasimpset -> int -> tactic
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val Clarsimp_tac: int -> tactic
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val mk_auto_tac : clasimpset -> int -> int -> tactic
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val auto_tac : clasimpset -> tactic
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val Auto_tac : tactic
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val auto : unit -> unit
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val force_tac : clasimpset -> int -> tactic
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val Force_tac : int -> tactic
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val force : int -> unit
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val change_global_css: (clasimpset * thm list -> clasimpset) -> theory attribute
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val change_local_css: (clasimpset * thm list -> clasimpset) -> Proof.context attribute
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val get_local_clasimpset: Proof.context -> clasimpset
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val clasimp_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list
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val setup : (theory -> theory) list
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end;
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functor ClasimpFun(Data: CLASIMP_DATA): CLASIMP =
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struct
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open Data;
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type claset = Classical.claset;
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type simpset = Simplifier.simpset;
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type clasimpset = claset * simpset;
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(* clasimpset operations *)
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(*this interface for updating a clasimpset is rudimentary and just for
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convenience for the most common cases*)
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fun pair_upd1 f ((a,b),x) = (f(a,x), b);
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fun pair_upd2 f ((a,b),x) = (a, f(b,x));
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fun op addSIs2 arg = pair_upd1 Classical.addSIs arg;
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fun op addSEs2 arg = pair_upd1 Classical.addSEs arg;
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fun op addSDs2 arg = pair_upd1 Classical.addSDs arg;
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fun op addIs2 arg = pair_upd1 Classical.addIs arg;
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fun op addEs2 arg = pair_upd1 Classical.addEs arg;
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fun op addDs2 arg = pair_upd1 Classical.addDs arg;
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fun op addsimps2 arg = pair_upd2 Simplifier.addsimps arg;
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fun op delsimps2 arg = pair_upd2 Simplifier.delsimps arg;
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(*not totally safe: may instantiate unknowns that appear also in other subgoals*)
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val safe_asm_full_simp_tac = Simplifier.generic_simp_tac true (true,true,true);
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(*Add a simpset to a classical set!*)
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(*Caution: only one simpset added can be added by each of addSss and addss*)
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fun cs addSss ss = Classical.addSaltern (cs, ("safe_asm_full_simp_tac",
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CHANGED o safe_asm_full_simp_tac ss));
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fun cs addss ss = Classical.addbefore (cs, ("asm_full_simp_tac",
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CHANGED o Simplifier.asm_full_simp_tac ss));
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(* tacticals *)
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fun CLASIMPSET tacf state =
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Classical.CLASET (fn cs => Simplifier.SIMPSET (fn ss => tacf (cs, ss))) state;
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fun CLASIMPSET' tacf i state =
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Classical.CLASET (fn cs => Simplifier.SIMPSET (fn ss => tacf (cs, ss) i)) state;
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fun clarsimp_tac (cs, ss) = safe_asm_full_simp_tac ss THEN_ALL_NEW
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Classical.clarify_tac (cs addSss ss);
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fun Clarsimp_tac i = clarsimp_tac (Classical.claset(), Simplifier.simpset()) i;
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(* auto_tac *)
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fun blast_depth_tac cs m i thm =
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Blast.depth_tac cs m i thm
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handle Blast.TRANS s => (warning ("Blast_tac: " ^ s); Seq.empty);
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(* a variant of depth_tac that avoids interference of the simplifier
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with dup_step_tac when they are combined by auto_tac *)
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local
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fun slow_step_tac' cs = Classical.appWrappers cs
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(Classical.instp_step_tac cs APPEND' Classical.haz_step_tac cs);
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in fun nodup_depth_tac cs m i state = SELECT_GOAL
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(Classical.safe_steps_tac cs 1 THEN_ELSE
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(DEPTH_SOLVE (nodup_depth_tac cs m 1),
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Classical.inst0_step_tac cs 1 APPEND COND (K (m=0)) no_tac
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(slow_step_tac' cs 1 THEN DEPTH_SOLVE (nodup_depth_tac cs (m-1) 1))
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)) i state;
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end;
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(*Designed to be idempotent, except if blast_depth_tac instantiates variables
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in some of the subgoals*)
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fun mk_auto_tac (cs, ss) m n =
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let val cs' = cs addss ss
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val maintac =
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blast_depth_tac cs m (* fast but can't use wrappers *)
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ORELSE'
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(CHANGED o nodup_depth_tac cs' n); (* slower but more general *)
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in EVERY [ALLGOALS (Simplifier.asm_full_simp_tac ss),
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TRY (Classical.safe_tac cs),
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REPEAT (FIRSTGOAL maintac),
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TRY (Classical.safe_tac (cs addSss ss)),
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prune_params_tac]
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end;
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fun auto_tac (cs,ss) = mk_auto_tac (cs,ss) 4 2;
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fun Auto_tac st = auto_tac (Classical.claset(), Simplifier.simpset()) st;
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fun auto () = by Auto_tac;
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(* force_tac *)
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(* aimed to solve the given subgoal totally, using whatever tools possible *)
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fun force_tac (cs,ss) = let val cs' = cs addss ss in SELECT_GOAL (EVERY [
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Classical.clarify_tac cs' 1,
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IF_UNSOLVED (Simplifier.asm_full_simp_tac ss 1),
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ALLGOALS (Classical.first_best_tac cs')]) end;
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fun Force_tac i = force_tac (Classical.claset(), Simplifier.simpset()) i;
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fun force i = by (Force_tac i);
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(* attributes *)
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fun change_global_css f (thy, th) =
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let
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val cs_ref = Classical.claset_ref_of thy;
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val ss_ref = Simplifier.simpset_ref_of thy;
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val (cs', ss') = f ((! cs_ref, ! ss_ref), [th]);
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in cs_ref := cs'; ss_ref := ss'; (thy, th) end;
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fun change_local_css f (ctxt, th) =
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let
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val cs = Classical.get_local_claset ctxt;
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val ss = Simplifier.get_local_simpset ctxt;
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val (cs', ss') = f ((cs, ss), [th]);
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val ctxt' =
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ctxt
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|> Classical.put_local_claset cs'
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|> Simplifier.put_local_simpset ss';
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in (ctxt', th) end;
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(* methods *)
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fun get_local_clasimpset ctxt =
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(Classical.get_local_claset ctxt, Simplifier.get_local_simpset ctxt);
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val clasimp_modifiers =
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Simplifier.simp_modifiers @ Splitter.split_modifiers @ Classical.cla_modifiers;
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fun clasimp_meth tac prems ctxt = Method.METHOD (fn facts =>
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ALLGOALS (Method.insert_tac (prems @ facts)) THEN tac (get_local_clasimpset ctxt));
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fun clasimp_meth' tac prems ctxt = Method.METHOD (fn facts =>
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HEADGOAL (Method.insert_tac (prems @ facts) THEN' tac (get_local_clasimpset ctxt)));
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val clasimp_method = Method.bang_sectioned_args clasimp_modifiers o clasimp_meth;
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val clasimp_method' = Method.bang_sectioned_args clasimp_modifiers o clasimp_meth';
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val setup =
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[Method.add_methods
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[("force", clasimp_method' force_tac, "force"),
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("auto", clasimp_method (CHANGED o auto_tac), "auto"),
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("clarsimp", clasimp_method' clarsimp_tac, "clarify simplified goal")]];
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end;
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